Quasi-static consideration of high-frequency modes for more efficient flexible multibody simulations

A number of sets of modes, for example eigenmodes, constraint modes, inertia-relief attachment modes, may be used to describe the linear elastic deformation of a flexible body in multibody dynamics. It is always possible to transform modes so that the conditions of the Buckens-frame are fulfilled. The latter frame leads to serious simplifications in the equations of motion, but cannot avoid a coupling between the body's rotational rigid body motion and its elastic deformation. In the present paper the deformation modes will be subdivided into low- and high-frequency modes. It will be shown that the latter-mentioned coupling effect of the second ones can be safely neglected in comparison with the first ones. Consequently, the high-frequency components can be removed from time integration at all, which leads to significant savings of computational effort while the accuracy regarding the body's deformation remains almost the same. In the case of a known frequency content of external excitation, an algorithm is given so that the available modes can be automatically separated into such low- and high-frequency modes. While the number of low-frequency modes remains more or less constant, there is a significant trend to use an increased number of high-frequency modes. Examples are moving loads (e.g.; guidance) or distributed loads as they occur in contact problems or when fluid pressure is acting on surfaces. A final numerical example is given in order to demonstrate the potential of the proposed method.